document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=285680>Question 285680</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At Ajax Spring Watewr, a half-liter bottle of soft dring is supposed to contain a mean of 520 ml. The filling process follows a normal distribution with a known process standard deviation of 4 ml. (a) which sampling distribution would you use if random samples of 10 bottles are to be weighed? Why? (b) Set up hypothesis and a two-tailed decision rule for the correct mean using the 5 percent level of significance. (c) I f a sample of 16 bottles shows a mean fill of 515 ml. does this contradict the hypothesis that the true mean is 520 ml?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #207100 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=207100\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> At Ajax Spring Water, a half-liter bottle of soft drink is supposed to contain a mean of 520 ml. The filling process follows a normal distribution with a known process standard deviation of 4 ml. <BR>\n" );
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document.write( "(a) which sampling distribution would you use if random samples of 10 bottles are to be weighed? Why?<BR>\n" );
document.write( "Note: Text books differ on whether a z or a t distribution should be used.<BR>\n" );
document.write( "Large numbers of the better stat teachers say we should use the t distribution<BR>\n" );
document.write( "on ALL tests of the population mean.  Others say use t only if the sample<BR>\n" );
document.write( "size is less that 30. <BR>\n" );
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document.write( "(b) Set up hypothesis and a two-tailed decision rule for the correct mean using the 5 percent level of significance.<BR>\n" );
document.write( "Ho: u = 520<BR>\n" );
document.write( "Ha: u is not equal to 520<BR>\n" );
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document.write( "Reject Ho if the test statistic is less than invT(0.025 with df = 9)=-2.2622<BR>\n" );
document.write( "or the test stat is greater than 2.2622)<BR>\n" );
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document.write( "(c) If a sample of 16 bottles shows a mean fill of 515 ml. does this contradict the hypothesis that the true mean is 520 ml?<BR>\n" );
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document.write( "t(515) = (515-520)/[4/sqrt(16)] = -5<BR>\n" );
document.write( "The critical values are +-invT(0.025 with df=15) = +-2.1314..<BR>\n" );
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document.write( "Conclusion: Since the test stat is in the reject interval, <BR>\n" );
document.write( "reject Ho that the mean is 520.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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